Which of the following numbers is a factor of 80? ${3,7,8,9,11}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $80$ by each of our answer choices. $80 \div 3 = 26\text{ R }2$ $80 \div 7 = 11\text{ R }3$ $80 \div 8 = 10$ $80 \div 9 = 8\text{ R }8$ $80 \div 11 = 7\text{ R }3$ The only answer choice that divides into $80$ with no remainder is $8$ $ 10$ $8$ $80$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $80$ $80 = 2\times2\times2\times2\times5 8 = 2\times2\times2$ Therefore the only factor of $80$ out of our choices is $8$. We can say that $80$ is divisible by $8$.